>Cantor's diagonal proof does *not* show the Reals are uncountable; it just >proves the much weaker statement that "the Reals cannot be listed".

Those two statements mean the *same* thing!

A "list" of objects is just a function that maps each natural numberto an object. To say that a set is listable is just to say that thereexists a list that contains all objects in the set. And that's exactlywhat it means to say that a set is countable.